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Mathematics
Mathematics
Problem
Suppose
f
f
f
is continuous on the closed interval
[
1
,
5
]
[1,5]
[
1
,
5
]
and its average value on that interval is
3.2
3.2
3.2
. Explain why there must exist a number
c
c
c
in
(
1
,
5
)
(1,5)
(
1
,
5
)
such that
f
(
c
)
=
3.2
f(c)=3.2
f
(
c
)
=
3.2
, and identify the theorem that guarantees this fact.
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